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convex set S on a plane, not lying on a line, is painted in p colors

Source: Romania TST 1995 2.4

February 17, 2020
combinatorial geometrycombinatoricsColoringconvex

Problem Statement

A convex set SS on a plane, not lying on a line, is painted in pp colors. Prove that for every n≥3n \ge 3 there exist infinitely many congruent nn-gons whose vertices are of the same color.
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